{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # 数据处理最重要的模块\n",
    "import pandas as pd # 数据处理最重要的模块\n",
    "import scipy.stats as stats # 统计模块\n",
    "import scipy\n",
    "# import pymysql  # 导入数据库模块\n",
    "\n",
    "\n",
    "#从datetime模块导入datetime类，用于处理日期和时间数据，可进行日期时间的创建、解析、运算等操作。\n",
    "from datetime import datetime # 时间模块\n",
    "\n",
    "\n",
    "#导入statsmodels库的公式接口模块，用于执行普通最小二乘法（OLS）回归等统计建模，方便通过公式形式指定回归模型。\n",
    "import statsmodels.formula.api as smf  # OLS regression\n",
    "\n",
    "# import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt  # 画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "\n",
    "from matplotlib.font_manager import FontProperties # 作图中文\n",
    "from pylab import mpl\n",
    "#mpl.rcParams['font.sans-serif'] = ['SimHei']\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "\n",
    "#设置输出的图表格式为矢量图（SVG），以保证图表清晰度。\n",
    "#输出矢量图 渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell # jupyter运行输出的模块\n",
    "#显示每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stock Market Return (Excess Return)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>MarketR_e</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>ret_e</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "      <th>Q</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.029998</td>\n",
       "      <td>0.036554</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.023068</td>\n",
       "      <td>0.029624</td>\n",
       "      <td>-0.084127</td>\n",
       "      <td>-0.305662</td>\n",
       "      <td>0.254049</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.010203</td>\n",
       "      <td>0.021860</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.003273</td>\n",
       "      <td>0.014930</td>\n",
       "      <td>-0.183573</td>\n",
       "      <td>-0.384745</td>\n",
       "      <td>0.241492</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>-0.099663</td>\n",
       "      <td>-0.060425</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>-0.106593</td>\n",
       "      <td>-0.067355</td>\n",
       "      <td>-0.252928</td>\n",
       "      <td>-0.445049</td>\n",
       "      <td>0.288857</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>-0.079652</td>\n",
       "      <td>-0.031449</td>\n",
       "      <td>0.006651</td>\n",
       "      <td>-0.086303</td>\n",
       "      <td>-0.038100</td>\n",
       "      <td>-0.234776</td>\n",
       "      <td>-0.394937</td>\n",
       "      <td>0.691749</td>\n",
       "      <td>1991 Q2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-05-31</th>\n",
       "      <td>-0.074521</td>\n",
       "      <td>0.005375</td>\n",
       "      <td>0.006092</td>\n",
       "      <td>-0.080613</td>\n",
       "      <td>-0.000717</td>\n",
       "      <td>-0.236294</td>\n",
       "      <td>0.181673</td>\n",
       "      <td>1.542701</td>\n",
       "      <td>1991 Q2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>-0.033685</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>-0.034803</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.227078</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.225960</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.070220</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.069102</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.045312</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.044194</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>-0.040799</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>-0.041917</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>408 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR  MarketR_e   rfmonth       ret     ret_e  marketret3  \\\n",
       "month                                                                       \n",
       "1991-01-31  0.029998   0.036554  0.006930  0.023068  0.029624   -0.084127   \n",
       "1991-02-28  0.010203   0.021860  0.006930  0.003273  0.014930   -0.183573   \n",
       "1991-03-31 -0.099663  -0.060425  0.006930 -0.106593 -0.067355   -0.252928   \n",
       "1991-04-30 -0.079652  -0.031449  0.006651 -0.086303 -0.038100   -0.234776   \n",
       "1991-05-31 -0.074521   0.005375  0.006092 -0.080613 -0.000717   -0.236294   \n",
       "...              ...        ...       ...       ...       ...         ...   \n",
       "2024-08-31 -0.031468  -0.033685  0.001118 -0.032586 -0.034803    0.151050   \n",
       "2024-09-30  0.195992   0.227078  0.001118  0.194874  0.225960    0.200147   \n",
       "2024-10-31 -0.003409   0.070220  0.001118 -0.004527  0.069102    0.000228   \n",
       "2024-11-30  0.009724   0.045312  0.001118  0.008606  0.044194         NaN   \n",
       "2024-12-31 -0.002679  -0.040799  0.001118 -0.003797 -0.041917         NaN   \n",
       "\n",
       "            marketret6  marketret12        Q  \n",
       "month                                         \n",
       "1991-01-31   -0.305662     0.254049  1991 Q1  \n",
       "1991-02-28   -0.384745     0.241492  1991 Q1  \n",
       "1991-03-31   -0.445049     0.288857  1991 Q1  \n",
       "1991-04-30   -0.394937     0.691749  1991 Q2  \n",
       "1991-05-31    0.181673     1.542701  1991 Q2  \n",
       "...                ...          ...      ...  \n",
       "2024-08-31         NaN          NaN  2024 Q3  \n",
       "2024-09-30         NaN          NaN  2024 Q3  \n",
       "2024-10-31         NaN          NaN  2024 Q4  \n",
       "2024-11-30         NaN          NaN  2024 Q4  \n",
       "2024-12-31         NaN          NaN  2024 Q4  \n",
       "\n",
       "[408 rows x 9 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#用于将日期调整为月末日期，确保时间序列的规整性\n",
    "from pandas.tseries.offsets import MonthEnd # 月末\n",
    "\n",
    "#读取2024年股票市场月度收益的CSV数据文件\n",
    "Market_ret = pd.read_csv('D:/笃行楼209/Marketret_mon_stock2024.csv')\n",
    "\n",
    "#将“month”列的日期字符串转换为datetime类型，并调整为当月月末日期。\n",
    "Market_ret['month'] = pd.to_datetime(Market_ret['month'], format='%b %Y') + MonthEnd(0)\n",
    "\n",
    "#将“month”列设为数据框的索引\n",
    "Market_ret.set_index('month', inplace=True)\n",
    "\n",
    "#按日期索引对数据进行升序排序，便于时间序列分析\n",
    "Market_ret.sort_index(inplace=True)\n",
    "\n",
    "#删除数据中名为“Unnamed: 0”的无意义列，清理数据结构\n",
    "Market_ret = Market_ret.drop(columns=['Unnamed: 0'])\n",
    "Market_ret"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inflation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cpi</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1987-01-31</th>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-02-28</th>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-03-31</th>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-04-30</th>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-05-31</th>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-03-31</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-04-30</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-05-31</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-06-30</th>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-07-31</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>463 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            cpi\n",
       "month          \n",
       "1987-01-31  5.1\n",
       "1987-02-28  5.4\n",
       "1987-03-31  5.8\n",
       "1987-04-30  6.7\n",
       "1987-05-31  7.6\n",
       "...         ...\n",
       "2025-03-31 -0.1\n",
       "2025-04-30 -0.1\n",
       "2025-05-31 -0.1\n",
       "2025-06-30  0.1\n",
       "2025-07-31  0.0\n",
       "\n",
       "[463 rows x 1 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inflation = pd.read_csv('D:/笃行楼209/inflation.csv')\n",
    "\n",
    "#将“month”列的日期字符串（格式为“年/月/日”）转换为datetime类型\n",
    "inflation['month'] = pd.to_datetime(inflation['month'],format='%Y/%m/%d')\n",
    "\n",
    "#将“month”列设为数据框的索引，使数据按时间维度组织\n",
    "inflation.set_index('month',inplace=True)\n",
    "inflation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 月度数据的预测\n",
    "\n",
    "A simple linear regression of an asset return on one or a few lagged predictors of interest is the most popular econometric approach for testing for return predictability. For simplicity, consider a univariate predictive regression of the period- $(t + 1)$ stock market return $r_{t+1}$ on a single predictor variable $x_t$:\n",
    "$$\n",
    "r_{t+1}=\\alpha+\\beta x_{t}+\\varepsilon_{t+1}\n",
    "$$\n",
    "where $\\varepsilon_{t+1}$ is a zero-mean, unpredictable disturbance term. When $x_t$ is the inflation rate, dividend yield, book-to-price ratio, or turnover. Many researchers find that $\\beta$ is significantly different from zero; that is, there is in-sample evidence of stock market return predictability.\n",
    "\n",
    "* H0:$\\beta = 0$\n",
    "* H1:$\\beta \\ne 0$(我们需要通过理论分析，得出$\\beta$的符号)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型： 通货膨胀与股票预期收益率\n",
    "\n",
    "$$\n",
    "r_{t+1} = \\alpha + \\beta*CPI_{t-1} + \\varepsilon_{t+1}\n",
    "$$\n",
    "\n",
    "两个假设：\n",
    "\n",
    "* H1： $\\beta > 0$\n",
    "\n",
    "* H2： $\\beta < 0$\n",
    "\n",
    "这是一个非常经典且重要的资产定价问题。通货膨胀与预期股票收益率之间的关系在金融学术界经过了数十年的广泛研究和激烈辩论，至今仍没有一个完全统一的定论。这恰恰是学术研究的魅力所在，即便是同一个问题，在不同的理论框架和实证检验下，也会得出看似矛盾的结论。\n",
    "\n",
    "---\n",
    "\n",
    "### **引言：经典的费雪假说**\n",
    "\n",
    "在深入探讨正反两方观点之前，我们必须先了解最基础的理论出发点——**欧文·费雪（Irving Fisher）的费雪效应**。在其最简单的形式中，名义利率等于真实利率加上预期的通货膨胀率。\n",
    "\n",
    "> 名义收益率 ≈ 真实收益率 + 预期通货膨胀率\n",
    "\n",
    "如果我们将这个逻辑应用到股票上，并假设股票的预期真实收益率是相对稳定的（因为它由经济体的基本生产力、风险偏好等真实变量决定），那么预期名义股票收益率应该随着预期通货膨胀率的上升而上升。这意味着，股票作为对公司实物资产（厂房、设备、存货）所有权的代表，其名义价值应该能够对冲通胀带来的货币贬值，从而保持其真实价值。\n",
    "\n",
    "这个直观且有力的理论，构成了两者正相关关系的核心基础。然而，大量的实证研究，尤其是在20世纪70年代之后，对这一经典假说提出了严峻的挑战。\n",
    "\n",
    "---\n",
    "\n",
    "### **一、 通货膨胀与预期股票收益率的正相关关系论述**\n",
    "\n",
    "支持两者存在正相关关系的逻辑主要建立在股票的“实物资产”属性上。\n",
    "\n",
    "1.  **理论逻辑：股票作为通胀的对冲工具（Inflation Hedge）**\n",
    "    *   **基本原理**：股票代表的是对公司所有权的索取权，而公司的价值根本上来自于其拥有的实物资产（Real Assets）和未来的盈利能力。在通胀环境下，产品和服务的价格会上涨，公司的名义收入和名义利润也随之增加。同时，公司拥有的厂房、土地、存货等实物资产的名义价值也会重估上升。因此，从理论上讲，股票的内在价值应该与物价水平同步上涨，从而使其名义收益率能够补偿通货膨胀带来的损失，保证投资者的真实回报。\n",
    "    *   **现金流折现模型视角**：在DCF模型中，通货膨胀会同时影响未来的名义现金流（分子）和名义折现率（分母）。如果通胀能够完全、无摩擦地传导至公司的产品售价和成本，并且名义折现率也根据费雪效应完全调整，那么股票的名义价格应该上升，以反映通胀。\n",
    "\n",
    "2.  **实证支持：长期视角下的发现**\n",
    "    *   早期的许多研究未能发现正相关关系，但这可能与研究的时间窗口有关。**[Boudoukh 和 Richardson (1993)](https://www.jstor.org/stable/2117566)** 的研究是一个重要的转折点。他们通过使用更长的时间序列数据（从19世纪至今），发现当考察的持有期越长（例如5年或更长），股票收益率与通货膨胀之间的正相关关系就越显著。\n",
    "    *   **结论启示**：他们的研究表明，股票在短期内可能不是一个好的通胀对冲工具，但在长期来看，其作为实物资产的保值属性会逐渐显现。这暗示了市场在短期内可能存在定价偏差或反应不足，但在长期会回归其基本面价值。\n",
    "\n",
    "---\n",
    "\n",
    "### **二、 通货膨胀与预期股票收益率的负相关关系论述**\n",
    "\n",
    "尽管正相关的理论直觉很强，但在20世纪下半叶，大量的实证研究（尤其是在美国市场）却惊人地发现两者之间存在稳健的**负相关**关系。这激发了金融学家们提出多种解释。\n",
    "\n",
    "1.  **理论逻辑与解释**\n",
    "    *   **税收效应（Tax Effect）**：这是最经典的解释之一。大多数国家的税法是基于**名义利润**和**名义资本利得**来征税的，而不是真实利润或真实资本利得。\n",
    "        *   **折旧**：在通胀期间，基于历史成本计算的设备折旧额，其真实价值会缩水，导致账面上的应税利润被高估。\n",
    "        *   **存货**：采用“先进先出”（FIFO）会计准则的公司，其销售成本会基于较早前购买的低成本存货，而收入则是按当前的高价格计算，这同样会虚增名义利润。\n",
    "        *   **资本利得税**：投资者卖出股票时，需要为名义上的价差缴税。即使股票价格的上涨仅仅是为了补偿通胀（真实收益为零），投资者依然要为这部分“虚假”的收益纳税。\n",
    "        这些税收上的扭曲效应，使得通货膨胀侵蚀了公司的真实税后利润和投资者的真实税后收益，从而降低了股票的吸引力，导致其价格下跌（即预期收益率与通胀负相关）。\n",
    "\n",
    "    *   **货币幻觉（Money Illusion）**：由诺贝尔奖得主 **Modigliani 和 Cohn (1979)** 提出的著名假说。他们认为，投资者在评估股票价值时会犯两个系统性错误：\n",
    "        1.  **错误的折现率**：投资者在用现金流折现模型估值时，倾向于使用名义利率去折现公司的真实现金流（未根据通胀调整的现金流），或者未能将公司因通胀而增加的债务价值（真实负债减少）考虑在内。这导致他们系统性地低估了股票的价值。\n",
    "        2.  **对盈利质量的误判**：投资者看到了公司报告的名义利润在增长，但未能充分认识到，在高通胀环境下，维持同样生产能力所需的资本重置成本也在急剧上升。因此，报告的利润质量实际上是下降的。\n",
    "        由于这种普遍存在的“货币幻觉”，当通胀上升时，市场会错误地压低股价。\n",
    "\n",
    "    *   **代理假说（Proxy Hypothesis）**：这是另一位诺贝尔奖得主 **Fama (1981)** 提出的一个更精巧的理论。他认为，股票收益率和通货膨胀之间的负相关关系是“伪相关”（Spurious Correlation），两者本身没有直接的因果联系。真正的关系是：\n",
    "        1.  股票收益率与**未来的实体经济活动**（如工业产出、GDP增长）**正相关**。因为股市是经济的晴雨表。\n",
    "        2.  通货膨胀率与**未来的实体经济活动**则呈现**负相关**。这在当时被称为“滞胀”（Stagflation）现象，即高通胀往往预示着未来经济的衰退。\n",
    "        3.  因此，股票收益率和通货膨胀率，因为它们都与同一个变量（未来经济活动）相关，但方向相反，从而表现出了表观上的负相关关系。通胀只是实体经济活动的“代理变量”。\n",
    "\n",
    "    *   **风险溢价与不确定性（Risk Premium & Uncertainty）**：高通胀时期往往伴随着更高的经济不确定性和政策不确定性（例如，央行会如何应对）。为了补偿这种增加的系统性风险，投资者会要求更高的风险溢价。在短期内，要求更高的预期回报率意味着更低的当前价格。因此，通胀的上升通过增加风险溢价，导致了当前股价的下跌。\n",
    "\n",
    "2.  **实证支持：里程碑式的研究**\n",
    "    *   **[Fama 和 Schwert (1977)](https://doi.org/10.1016/0304-405X(77)90014-9)** 的研究是该领域的里程碑。他们检验了1953-1971年的美国数据，发现股票收益率与预期通胀、未预期通胀以及通胀变化都存在显著的负相关关系。他们明确指出，股票在那个时期是一个“坏”的通胀对冲工具，其表现甚至不如短期国债。这项研究的结论主导了学术界很长一段时间的看法。\n",
    "\n",
    "---\n",
    "\n",
    "### **总结与学术洞察**\n",
    "\n",
    "总结一下：通货膨胀与预期股票收益率的关系远非“一对一”的简单映射。它取决于多种因素的复杂互动：\n",
    "\n",
    "1.  **时间跨度**：在短期，税收效应、不确定性和市场非理性（如货币幻觉）可能占据主导，导致负相关。但在长期，股票作为实物资产的对冲属性可能最终显现，呈现正相关。\n",
    "2.  **通胀的来源和性质**：由需求拉动的温和通胀（Demand-Pull Inflation）可能伴随着经济繁荣，对股价有利。而由成本推动的通胀（Cost-Push Inflation），如石油危机，则会损害企业利润，对股价不利。\n",
    "3.  **制度因素**：税法的设计、会计准则的选择以及央行的政策反应框架，都会深刻影响这一关系。例如，如果税法改革为通胀进行指数化调整，那么负相关的税收效应就会减弱。\n",
    "4.  **研究样本与时期**：20世纪70-80年代的“大滞胀”时期，负相关关系尤为明显。但在其他历史时期或不同国家，这种关系可能不那么稳定。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>MarketR_e</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>ret_e</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "      <th>Q</th>\n",
       "      <th>cpi</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.029998</td>\n",
       "      <td>0.036554</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.023068</td>\n",
       "      <td>0.029624</td>\n",
       "      <td>-0.084127</td>\n",
       "      <td>-0.305662</td>\n",
       "      <td>0.254049</td>\n",
       "      <td>1991 Q1</td>\n",
       "      <td>2.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.010203</td>\n",
       "      <td>0.021860</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.003273</td>\n",
       "      <td>0.014930</td>\n",
       "      <td>-0.183573</td>\n",
       "      <td>-0.384745</td>\n",
       "      <td>0.241492</td>\n",
       "      <td>1991 Q1</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>-0.099663</td>\n",
       "      <td>-0.060425</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>-0.106593</td>\n",
       "      <td>-0.067355</td>\n",
       "      <td>-0.252928</td>\n",
       "      <td>-0.445049</td>\n",
       "      <td>0.288857</td>\n",
       "      <td>1991 Q1</td>\n",
       "      <td>1.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>-0.079652</td>\n",
       "      <td>-0.031449</td>\n",
       "      <td>0.006651</td>\n",
       "      <td>-0.086303</td>\n",
       "      <td>-0.038100</td>\n",
       "      <td>-0.234776</td>\n",
       "      <td>-0.394937</td>\n",
       "      <td>0.691749</td>\n",
       "      <td>1991 Q2</td>\n",
       "      <td>1.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-05-31</th>\n",
       "      <td>-0.074521</td>\n",
       "      <td>0.005375</td>\n",
       "      <td>0.006092</td>\n",
       "      <td>-0.080613</td>\n",
       "      <td>-0.000717</td>\n",
       "      <td>-0.236294</td>\n",
       "      <td>0.181673</td>\n",
       "      <td>1.542701</td>\n",
       "      <td>1991 Q2</td>\n",
       "      <td>3.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>-0.033685</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>-0.034803</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.227078</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.225960</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.070220</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.069102</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.045312</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.044194</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>-0.040799</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>-0.041917</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>408 rows × 10 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR  MarketR_e   rfmonth       ret     ret_e  marketret3  \\\n",
       "month                                                                       \n",
       "1991-01-31  0.029998   0.036554  0.006930  0.023068  0.029624   -0.084127   \n",
       "1991-02-28  0.010203   0.021860  0.006930  0.003273  0.014930   -0.183573   \n",
       "1991-03-31 -0.099663  -0.060425  0.006930 -0.106593 -0.067355   -0.252928   \n",
       "1991-04-30 -0.079652  -0.031449  0.006651 -0.086303 -0.038100   -0.234776   \n",
       "1991-05-31 -0.074521   0.005375  0.006092 -0.080613 -0.000717   -0.236294   \n",
       "...              ...        ...       ...       ...       ...         ...   \n",
       "2024-08-31 -0.031468  -0.033685  0.001118 -0.032586 -0.034803    0.151050   \n",
       "2024-09-30  0.195992   0.227078  0.001118  0.194874  0.225960    0.200147   \n",
       "2024-10-31 -0.003409   0.070220  0.001118 -0.004527  0.069102    0.000228   \n",
       "2024-11-30  0.009724   0.045312  0.001118  0.008606  0.044194         NaN   \n",
       "2024-12-31 -0.002679  -0.040799  0.001118 -0.003797 -0.041917         NaN   \n",
       "\n",
       "            marketret6  marketret12        Q  cpi  \n",
       "month                                              \n",
       "1991-01-31   -0.305662     0.254049  1991 Q1  2.2  \n",
       "1991-02-28   -0.384745     0.241492  1991 Q1  1.0  \n",
       "1991-03-31   -0.445049     0.288857  1991 Q1  1.6  \n",
       "1991-04-30   -0.394937     0.691749  1991 Q2  1.3  \n",
       "1991-05-31    0.181673     1.542701  1991 Q2  3.6  \n",
       "...                ...          ...      ...  ...  \n",
       "2024-08-31         NaN          NaN  2024 Q3  0.6  \n",
       "2024-09-30         NaN          NaN  2024 Q3  0.4  \n",
       "2024-10-31         NaN          NaN  2024 Q4  0.3  \n",
       "2024-11-30         NaN          NaN  2024 Q4  0.2  \n",
       "2024-12-31         NaN          NaN  2024 Q4  0.1  \n",
       "\n",
       "[408 rows x 10 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#通过 pandas 的 merge 函数，以两个数据框的日期索引为依据\n",
    "#左连接（how='left'）合并Market_ret（股票市场收益数据）和inflation（通货膨胀数据）\n",
    "#得到用于后续回归分析的整合数据集 reg_data 。\n",
    "\n",
    "reg_data = pd.merge(Market_ret, inflation, left_index=True, right_index=True,how='left')\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 导出数据\n",
    "reg_data.to_csv('D:/笃行楼209/reg_data.csv')\n",
    "# save as excel\n",
    "reg_data.to_excel('D:/笃行楼209/reg_data.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg_data = reg_data['2015':]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 作图 Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"652.78125pt\" height=\"339.168125pt\" viewBox=\"0 0 652.78125 339.168125\" xmlns=\"http://www.w3.org/2000/svg\" version=\"1.1\">\n",
       " <metadata>\n",
       "  <rdf:RDF xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n",
       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2025-10-16T21:32:38.651504</dc:date>\n",
       "    <dc:format>image/svg+xml</dc:format>\n",
       "    <dc:creator>\n",
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       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the China's stock market return and inflation into one graph\n",
    "fig, ax1 = plt.subplots(figsize=(10,5))\n",
    "# the linewidth and marker size are set to be very small\n",
    "ax1.plot(reg_data['ret'],color='orange',marker='.',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='--',label='China Stock Market Return')\n",
    "ax1.set_ylabel('China Stock Market Return',color='green')\n",
    "#ax1.set_xlabel('Month')\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(reg_data['cpi'].shift(2),color='blue',marker='*',linewidth=0.8,\n",
    "         markersize=4,\n",
    "         linestyle='-',label='China Inflation')\n",
    "\n",
    "ax2.set_ylabel('China Inflation',color='red')\n",
    "\n",
    "plt.title('China Stock Market Return and Inflation')\n",
    "\n",
    "# change the legend into one box\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "# save figure\n",
    "fig.savefig('D:/笃行楼209/Pictures/China Stock Market Return and Inflation.png',dpi = 1000,bbox_inches='tight')\n",
    "\n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 描述性统计 Summary\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ret</th>\n",
       "      <th>cpi</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>120.00000</td>\n",
       "      <td>120.00000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.00353</td>\n",
       "      <td>1.58697</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.06166</td>\n",
       "      <td>1.15353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.25064</td>\n",
       "      <td>-0.80000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>-0.02508</td>\n",
       "      <td>0.79095</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.00146</td>\n",
       "      <td>1.63450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.02915</td>\n",
       "      <td>2.27838</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.19487</td>\n",
       "      <td>5.38460</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             ret        cpi\n",
       "count  120.00000  120.00000\n",
       "mean     0.00353    1.58697\n",
       "std      0.06166    1.15353\n",
       "min     -0.25064   -0.80000\n",
       "25%     -0.02508    0.79095\n",
       "50%      0.00146    1.63450\n",
       "75%      0.02915    2.27838\n",
       "max      0.19487    5.38460"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 主要变量（ret, cpi）的描述性统计\n",
    "reg_data[['ret','cpi']].describe().round(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.01838592944164657"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "3.169024932447619"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data['ret'].skew()\n",
    "reg_data['ret'].kurt()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "原始序列的ADF检验结果:\n",
      "ADF Statistic: -8.2104\n",
      "p-value: 0.0000\n",
      "Critical Values:\n",
      "   1%: -3.4870\n",
      "   5%: -2.8864\n",
      "   10%: -2.5800\n",
      "结论: p-value小于0.05，拒绝原假设，序列是平稳的。\n"
     ]
    }
   ],
   "source": [
    "#导入 statsmodels 库中的ADF检验工具，用于判断时间序列是否平稳\n",
    "from statsmodels.tsa.stattools import adfuller as ADF\n",
    "\n",
    "# 对月收益率数据进行ADF检验\n",
    "adf_result = ADF(reg_data['ret'])\n",
    "\n",
    "\n",
    "#ADF Statistic（ADF统计量）、p-value（概率值）、Critical Values（临界值）\n",
    "#并根据p-value与0.05的大小关系，判断序列是否平稳（p-value≤0.05则序列平稳，否则非平稳）\n",
    "print('原始序列的ADF检验结果:')\n",
    "print(f'ADF Statistic: {adf_result[0]:.4f}')\n",
    "print(f'p-value: {adf_result[1]:.4f}')\n",
    "print('Critical Values:')\n",
    "for key, value in adf_result[4].items():\n",
    "    print(f'   {key}: {value:.4f}')\n",
    "\n",
    "if adf_result[1] <= 0.05:\n",
    "    print('结论: p-value小于0.05，拒绝原假设，序列是平稳的。')\n",
    "else:\n",
    "    print('结论: p-value大于0.05，未能拒绝原假设，序列是非平稳的。')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "原始序列的ADF检验结果:\n",
      "ADF Statistic: -1.0268\n",
      "p-value: 0.7433\n",
      "Critical Values:\n",
      "   1%: -3.4936\n",
      "   5%: -2.8892\n",
      "   10%: -2.5815\n",
      "结论: p-value大于0.05，未能拒绝原假设，序列是非平稳的。\n"
     ]
    }
   ],
   "source": [
    "#筛选出reg_data中2015年及之后的数据\n",
    "adf_result = ADF(reg_data['2015':]['cpi'])\n",
    "\n",
    "#输出统计量、p值和临界值。\n",
    "#通过 if adf_result[1] <= 0.05判断：\n",
    "#p值 ≤ 0.05 → 拒绝“存在单位根”的原假设 → 序列平稳。\n",
    "# p值 > 0.05 → 不能拒绝原假设 → 序列非平稳。\n",
    " \n",
    "print('\\n原始序列的ADF检验结果:')\n",
    "print(f'ADF Statistic: {adf_result[0]:.4f}')\n",
    "print(f'p-value: {adf_result[1]:.4f}')\n",
    "print('Critical Values:')\n",
    "for key, value in adf_result[4].items():\n",
    "    print(f'   {key}: {value:.4f}')\n",
    "\n",
    "if adf_result[1] <= 0.05:\n",
    "    print('结论: p-value小于0.05，拒绝原假设，序列是平稳的。')\n",
    "else:\n",
    "    print('结论: p-value大于0.05，未能拒绝原假设，序列是非平稳的。')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS 回归结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.000\n",
      "Model:                            OLS   Adj. R-squared:                 -0.009\n",
      "Method:                 Least Squares   F-statistic:                   0.02471\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):              0.875\n",
      "Time:                        21:32:42   Log-Likelihood:                 161.05\n",
      "No. Observations:                 118   AIC:                            -318.1\n",
      "Df Residuals:                     116   BIC:                            -312.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0025      0.007      0.375      0.708      -0.011       0.016\n",
      "lcpi           0.0397      0.253      0.157      0.875      -0.456       0.535\n",
      "==============================================================================\n",
      "Omnibus:                       13.110   Durbin-Watson:                   1.685\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               42.294\n",
      "Skew:                           0.000   Prob(JB):                     6.54e-10\n",
      "Kurtosis:                       5.933   Cond. No.                         87.5\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\admin\\AppData\\Local\\Temp\\ipykernel_11604\\3149098646.py:6: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  reg_data['lcpi'] = reg_data['cpi'].shift(2)/100\n"
     ]
    }
   ],
   "source": [
    "# Regression of return on inflation\n",
    "\n",
    "#构建滞后通胀变量\n",
    "#以2015年1月至2024年12月的reg_data为数据集，构建“收益率（ret）对滞后通胀（lcpi）”的普通最小二乘法（OLS）回归模型\n",
    "#cov_type='HAC'和maxlags=6是为了采用异方差自相关一致（HAC）的标准误估计，解决时间序列数据中常见的异方差和自相关问题，使回归结果更稳健。\n",
    "reg_data['lcpi'] = reg_data['cpi'].shift(2)/100\n",
    "model_cpi = smf.ols('ret ~ lcpi',\n",
    "                 data=reg_data['2015-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.021\n",
      "Model:                            OLS   Adj. R-squared:                  0.004\n",
      "Method:                 Least Squares   F-statistic:                    0.6630\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):              0.517\n",
      "Time:                        21:32:43   Log-Likelihood:                 162.31\n",
      "No. Observations:                 118   AIC:                            -318.6\n",
      "Df Residuals:                     115   BIC:                            -310.3\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0020      0.006      0.331      0.741      -0.010       0.014\n",
      "lcpi           0.0412      0.232      0.177      0.859      -0.414       0.496\n",
      "lret           0.1455      0.128      1.136      0.256      -0.106       0.397\n",
      "==============================================================================\n",
      "Omnibus:                       13.502   Durbin-Watson:                   1.934\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               44.951\n",
      "Skew:                          -0.023   Prob(JB):                     1.73e-10\n",
      "Kurtosis:                       6.023   Cond. No.                         87.5\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\admin\\AppData\\Local\\Temp\\ipykernel_11604\\2798743529.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  reg_data['lret'] = reg_data['ret'].shift(1)\n"
     ]
    }
   ],
   "source": [
    "#构建收益率滞后变量\n",
    "reg_data['lret'] = reg_data['ret'].shift(1)\n",
    "\n",
    "#执行多变量OLS回归\n",
    "#以2015年1月至2024年12月的reg_data为数据集\n",
    "#构建“当前收益率（ret）对滞后通胀（lcpi）和滞后收益率（lret）”的普通最小二乘法（OLS）回归模型\n",
    "#cov_type='HAC'和maxlags=6采用异方差自相关一致（HAC）标准误估计，解决时间序列数据的异方差和自相关问题，保证回归结果的稳健性。\n",
    "model_cpi_lag = smf.ols('ret ~ lcpi + lret',\n",
    "                 data=reg_data['2015-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi_lag.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 预期收益率 Expected Return / Conditional Return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
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   ],
   "source": [
    "#筛选2015年1月至2024年12月的数据集并复制，避免原数据被修改\n",
    "data = reg_data['2015-01':'2024-12'].copy()\n",
    "\n",
    "#将回归模型model_cpi的拟合收益率值存入新列fitted_return，用于后续绘图对比\n",
    "data['fitted_return'] =  model_cpi.fittedvalues\n",
    "\n",
    "fig = plt.figure(figsize=(10, 5))\n",
    "plt.plot('ret',\n",
    "         '-r',\n",
    "         label='ret',\n",
    "         linewidth=1,\n",
    "         data=data)\n",
    "plt.plot('fitted_return',\n",
    "         '-b',\n",
    "         label='Fitted Return',\n",
    "         linewidth=1,\n",
    "         data=data)\n",
    "plt.title(\"China's Stock Market\")\n",
    "plt.xlabel('Month')  # 画图的x轴名称\n",
    "plt.ylabel('Return')  # 画图的y轴名称\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "plt.legend()\n",
    "fig.savefig('D:/笃行楼209/Pictures/fitted_return.pdf', bbox_inches='tight')  # 更改输出图片格式 jpg\n",
    "plt.show();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 季度结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<style scoped>\n",
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       "    }\n",
       "\n",
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       "    }\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ret</th>\n",
       "      <th>cpi</th>\n",
       "      <th>lag_cpi</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-03-31</th>\n",
       "      <td>0.213475</td>\n",
       "      <td>3.570700e+00</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-06-30</th>\n",
       "      <td>0.173177</td>\n",
       "      <td>4.130800e+00</td>\n",
       "      <td>3.570700e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-09-30</th>\n",
       "      <td>-0.312440</td>\n",
       "      <td>5.198300e+00</td>\n",
       "      <td>4.130800e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-12-31</th>\n",
       "      <td>0.226691</td>\n",
       "      <td>4.390000e+00</td>\n",
       "      <td>5.198300e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-03-31</th>\n",
       "      <td>-0.165603</td>\n",
       "      <td>6.337500e+00</td>\n",
       "      <td>4.390000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-06-30</th>\n",
       "      <td>-0.003627</td>\n",
       "      <td>6.246400e+00</td>\n",
       "      <td>6.337500e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-09-30</th>\n",
       "      <td>0.031311</td>\n",
       "      <td>5.025100e+00</td>\n",
       "      <td>6.246400e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-12-31</th>\n",
       "      <td>0.018354</td>\n",
       "      <td>6.424700e+00</td>\n",
       "      <td>5.025100e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-03-31</th>\n",
       "      <td>0.027334</td>\n",
       "      <td>4.268200e+00</td>\n",
       "      <td>6.424700e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-06-30</th>\n",
       "      <td>-0.005502</td>\n",
       "      <td>4.178700e+00</td>\n",
       "      <td>4.268200e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-09-30</th>\n",
       "      <td>0.061479</td>\n",
       "      <td>4.805900e+00</td>\n",
       "      <td>4.178700e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-12-31</th>\n",
       "      <td>-0.014987</td>\n",
       "      <td>5.451200e+00</td>\n",
       "      <td>4.805900e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-03-31</th>\n",
       "      <td>-0.037339</td>\n",
       "      <td>6.428600e+00</td>\n",
       "      <td>5.451200e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-06-30</th>\n",
       "      <td>-0.111533</td>\n",
       "      <td>5.406400e+00</td>\n",
       "      <td>6.428600e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-09-30</th>\n",
       "      <td>-0.024770</td>\n",
       "      <td>6.834900e+00</td>\n",
       "      <td>5.406400e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2018-12-31</th>\n",
       "      <td>-0.122870</td>\n",
       "      <td>6.578900e+00</td>\n",
       "      <td>6.834900e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-03-31</th>\n",
       "      <td>0.265317</td>\n",
       "      <td>5.503600e+00</td>\n",
       "      <td>6.578900e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-06-30</th>\n",
       "      <td>-0.040141</td>\n",
       "      <td>7.964100e+00</td>\n",
       "      <td>5.503600e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-09-30</th>\n",
       "      <td>-0.008988</td>\n",
       "      <td>8.649100e+00</td>\n",
       "      <td>7.964100e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2019-12-31</th>\n",
       "      <td>0.060801</td>\n",
       "      <td>1.269870e+01</td>\n",
       "      <td>8.649100e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-03-31</th>\n",
       "      <td>-0.080256</td>\n",
       "      <td>1.482950e+01</td>\n",
       "      <td>1.269870e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-06-30</th>\n",
       "      <td>0.124221</td>\n",
       "      <td>8.213100e+00</td>\n",
       "      <td>1.482950e+01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-09-30</th>\n",
       "      <td>0.092409</td>\n",
       "      <td>6.771500e+00</td>\n",
       "      <td>8.213100e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2020-12-31</th>\n",
       "      <td>0.077205</td>\n",
       "      <td>2.000000e-01</td>\n",
       "      <td>6.771500e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-03-31</th>\n",
       "      <td>-0.025353</td>\n",
       "      <td>-1.000000e-01</td>\n",
       "      <td>2.000000e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-06-30</th>\n",
       "      <td>0.066429</td>\n",
       "      <td>3.300000e+00</td>\n",
       "      <td>-1.000000e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-09-30</th>\n",
       "      <td>-0.003805</td>\n",
       "      <td>2.500000e+00</td>\n",
       "      <td>3.300000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2021-12-31</th>\n",
       "      <td>0.032499</td>\n",
       "      <td>5.300000e+00</td>\n",
       "      <td>2.500000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-03-31</th>\n",
       "      <td>-0.127150</td>\n",
       "      <td>3.300000e+00</td>\n",
       "      <td>5.300000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-06-30</th>\n",
       "      <td>0.051597</td>\n",
       "      <td>6.730400e+00</td>\n",
       "      <td>3.300000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-09-30</th>\n",
       "      <td>-0.114140</td>\n",
       "      <td>8.000000e+00</td>\n",
       "      <td>6.730400e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2022-12-31</th>\n",
       "      <td>0.022921</td>\n",
       "      <td>5.500000e+00</td>\n",
       "      <td>8.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-03-31</th>\n",
       "      <td>0.058373</td>\n",
       "      <td>3.800000e+00</td>\n",
       "      <td>5.500000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-06-30</th>\n",
       "      <td>-0.021804</td>\n",
       "      <td>3.000000e-01</td>\n",
       "      <td>3.800000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.030355</td>\n",
       "      <td>-2.000000e-01</td>\n",
       "      <td>3.000000e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.047820</td>\n",
       "      <td>-1.000000e+00</td>\n",
       "      <td>-2.000000e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.006789</td>\n",
       "      <td>-8.326673e-17</td>\n",
       "      <td>-1.000000e+00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.034157</td>\n",
       "      <td>8.000000e-01</td>\n",
       "      <td>-8.326673e-17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.155216</td>\n",
       "      <td>1.500000e+00</td>\n",
       "      <td>8.000000e-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.000228</td>\n",
       "      <td>6.000000e-01</td>\n",
       "      <td>1.500000e+00</td>\n",
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      ],
      "text/plain": [
       "                 ret           cpi       lag_cpi\n",
       "month                                           \n",
       "2015-03-31  0.213475  3.570700e+00           NaN\n",
       "2015-06-30  0.173177  4.130800e+00  3.570700e+00\n",
       "2015-09-30 -0.312440  5.198300e+00  4.130800e+00\n",
       "2015-12-31  0.226691  4.390000e+00  5.198300e+00\n",
       "2016-03-31 -0.165603  6.337500e+00  4.390000e+00\n",
       "2016-06-30 -0.003627  6.246400e+00  6.337500e+00\n",
       "2016-09-30  0.031311  5.025100e+00  6.246400e+00\n",
       "2016-12-31  0.018354  6.424700e+00  5.025100e+00\n",
       "2017-03-31  0.027334  4.268200e+00  6.424700e+00\n",
       "2017-06-30 -0.005502  4.178700e+00  4.268200e+00\n",
       "2017-09-30  0.061479  4.805900e+00  4.178700e+00\n",
       "2017-12-31 -0.014987  5.451200e+00  4.805900e+00\n",
       "2018-03-31 -0.037339  6.428600e+00  5.451200e+00\n",
       "2018-06-30 -0.111533  5.406400e+00  6.428600e+00\n",
       "2018-09-30 -0.024770  6.834900e+00  5.406400e+00\n",
       "2018-12-31 -0.122870  6.578900e+00  6.834900e+00\n",
       "2019-03-31  0.265317  5.503600e+00  6.578900e+00\n",
       "2019-06-30 -0.040141  7.964100e+00  5.503600e+00\n",
       "2019-09-30 -0.008988  8.649100e+00  7.964100e+00\n",
       "2019-12-31  0.060801  1.269870e+01  8.649100e+00\n",
       "2020-03-31 -0.080256  1.482950e+01  1.269870e+01\n",
       "2020-06-30  0.124221  8.213100e+00  1.482950e+01\n",
       "2020-09-30  0.092409  6.771500e+00  8.213100e+00\n",
       "2020-12-31  0.077205  2.000000e-01  6.771500e+00\n",
       "2021-03-31 -0.025353 -1.000000e-01  2.000000e-01\n",
       "2021-06-30  0.066429  3.300000e+00 -1.000000e-01\n",
       "2021-09-30 -0.003805  2.500000e+00  3.300000e+00\n",
       "2021-12-31  0.032499  5.300000e+00  2.500000e+00\n",
       "2022-03-31 -0.127150  3.300000e+00  5.300000e+00\n",
       "2022-06-30  0.051597  6.730400e+00  3.300000e+00\n",
       "2022-09-30 -0.114140  8.000000e+00  6.730400e+00\n",
       "2022-12-31  0.022921  5.500000e+00  8.000000e+00\n",
       "2023-03-31  0.058373  3.800000e+00  5.500000e+00\n",
       "2023-06-30 -0.021804  3.000000e-01  3.800000e+00\n",
       "2023-09-30 -0.030355 -2.000000e-01  3.000000e-01\n",
       "2023-12-31 -0.047820 -1.000000e+00 -2.000000e-01\n",
       "2024-03-31  0.006789 -8.326673e-17 -1.000000e+00\n",
       "2024-06-30 -0.034157  8.000000e-01 -8.326673e-17\n",
       "2024-09-30  0.155216  1.500000e+00  8.000000e-01\n",
       "2024-12-31  0.000228  6.000000e-01  1.500000e+00"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#选择1995年1月到2024年12月的数据。按季度（QE表示end of quarter）重采样。\n",
    "#用(1 + x).prod() - 1计算季度累计收益（复利）\n",
    "#用sum(x)计算季度通胀之和\n",
    "Q_reg_data = reg_data['1995-01':'2024-12'].resample('Q').apply({\n",
    "    'ret':\n",
    "    lambda x: (1 + x).prod() - 1,\n",
    "    'cpi':\n",
    "    lambda x: sum(x)\n",
    "})\n",
    "Q_reg_data['lag_cpi'] = Q_reg_data['cpi'].shift(1)\n",
    "#把cpi列后移1期，得到上一季度的通胀，用于后续回归分析\n",
    "\n",
    "Q_reg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Solarize_Light2',\n",
       " '_classic_test_patch',\n",
       " '_mpl-gallery',\n",
       " '_mpl-gallery-nogrid',\n",
       " 'bmh',\n",
       " 'classic',\n",
       " 'dark_background',\n",
       " 'fast',\n",
       " 'fivethirtyeight',\n",
       " 'ggplot',\n",
       " 'grayscale',\n",
       " 'seaborn-v0_8',\n",
       " 'seaborn-v0_8-bright',\n",
       " 'seaborn-v0_8-colorblind',\n",
       " 'seaborn-v0_8-dark',\n",
       " 'seaborn-v0_8-dark-palette',\n",
       " 'seaborn-v0_8-darkgrid',\n",
       " 'seaborn-v0_8-deep',\n",
       " 'seaborn-v0_8-muted',\n",
       " 'seaborn-v0_8-notebook',\n",
       " 'seaborn-v0_8-paper',\n",
       " 'seaborn-v0_8-pastel',\n",
       " 'seaborn-v0_8-poster',\n",
       " 'seaborn-v0_8-talk',\n",
       " 'seaborn-v0_8-ticks',\n",
       " 'seaborn-v0_8-white',\n",
       " 'seaborn-v0_8-whitegrid',\n",
       " 'tableau-colorblind10']"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#用于获取当前Matplotlib库中所有可用的绘图风格列表\n",
    "plt.style.available"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
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    "# Change the figure style\n",
    "plt.style.use('classic')\n",
    "fig = plt.figure(figsize=(8, 4))\n",
    "ax1 = fig.add_subplot(1, 1, 1)  #(x, x, x)这里前两个表示几*几的网格，最后一个表示第几子图\n",
    "\n",
    "ax1.plot(Q_reg_data['ret'],\n",
    "         color='blue',\n",
    "         marker='.',\n",
    "         linestyle='-',\n",
    "         linewidth=1,\n",
    "         markersize=6,\n",
    "         alpha=0.4,\n",
    "         label='Market Return')\n",
    "ax1.set_xlabel('Q')  # 设置横坐标标签\n",
    "ax1.set_ylabel('return')  # 设置左边纵坐标标签\n",
    "#ax1.legend(loc=2)  # 设置图例在左上方\n",
    "ax1.set_title(\"CPI and China's stock market excess return: Quarterly 1995-2024\")  # 给整张图命名\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "plt.xticks(rotation = 90) # 转置x轴的日期显示格式\n",
    "\n",
    "ax2 = ax1.twinx()  #twinx()函数表示共享x轴\n",
    "ax2.plot(Q_reg_data['lag_cpi'],\n",
    "         color='red',\n",
    "         marker='o',\n",
    "         linestyle='-',\n",
    "         linewidth=1,\n",
    "         markersize=2,\n",
    "         alpha=0.7,\n",
    "         label='CPI')\n",
    "ax2.set_ylabel('CPI')  # 设置右边纵坐标标签\n",
    "#ax2.legend(loc=1)  # 设置图例在右上方\n",
    "\n",
    "# change the legend into one box\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "fig.savefig('Qcpi.pdf', bbox_inches='tight')\n",
    "plt.show();"
   ]
  },
  {
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   "execution_count": 18,
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    {
     "name": "stdout",
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     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.004\n",
      "Model:                            OLS   Adj. R-squared:                 -0.023\n",
      "Method:                 Least Squares   F-statistic:                    0.3668\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):              0.548\n",
      "Time:                        21:32:52   Log-Likelihood:                 32.911\n",
      "No. Observations:                  39   AIC:                            -61.82\n",
      "Df Residuals:                      37   BIC:                            -58.49\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0038      0.017     -0.223      0.824      -0.038       0.030\n",
      "lcpi           0.0019      0.003      0.606      0.545      -0.004       0.008\n",
      "==============================================================================\n",
      "Omnibus:                        4.062   Durbin-Watson:                   2.975\n",
      "Prob(Omnibus):                  0.131   Jarque-Bera (JB):                3.676\n",
      "Skew:                          -0.166   Prob(JB):                        0.159\n",
      "Kurtosis:                       4.467   Cond. No.                         10.7\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 2 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "Q_reg_data['lcpi'] = Q_reg_data['cpi'].shift(1)\n",
    "model_qcpi = smf.ols('ret ~ lcpi',\n",
    "                 data=Q_reg_data['2015':'2024']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "print(model_qcpi.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.172\n",
      "Model:                            OLS   Adj. R-squared:                  0.126\n",
      "Method:                 Least Squares   F-statistic:                     3.419\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):             0.0437\n",
      "Time:                        21:32:53   Log-Likelihood:                 36.509\n",
      "No. Observations:                  39   AIC:                            -67.02\n",
      "Df Residuals:                      36   BIC:                            -62.03\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0062      0.019      0.333      0.739      -0.030       0.043\n",
      "lcpi           0.0008      0.003      0.225      0.822      -0.006       0.008\n",
      "lret          -0.3924      0.154     -2.547      0.011      -0.694      -0.090\n",
      "==============================================================================\n",
      "Omnibus:                        2.058   Durbin-Watson:                   2.155\n",
      "Prob(Omnibus):                  0.357   Jarque-Bera (JB):                1.079\n",
      "Skew:                           0.119   Prob(JB):                        0.583\n",
      "Kurtosis:                       3.779   Cond. No.                         54.6\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 2 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "Q_reg_data['lret'] = Q_reg_data['ret'].shift(1)\n",
    "model_qcpi_lag = smf.ols('ret ~ lcpi + lret',\n",
    "                 data=Q_reg_data['2015':'2024']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 2})\n",
    "print(model_qcpi_lag.summary())"
   ]
  },
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   "execution_count": 20,
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       "    </g>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
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       "   <rect x=\"56.953125\" y=\"23.14175\" width=\"558\" height=\"288\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = Q_reg_data['2015-01':'2024-12'].copy()\n",
    "data['fitted_return'] =  model_cpi.fittedvalues\n",
    "\n",
    "fig = plt.figure(figsize=(10, 5))\n",
    "plt.plot('ret',\n",
    "         '-r',\n",
    "         label='ret',\n",
    "         linewidth=1,\n",
    "         data=data)\n",
    "plt.plot('fitted_return',\n",
    "         '-b',\n",
    "         label='Fitted Return',\n",
    "         linewidth=1,\n",
    "         data=data)\n",
    "plt.title(\"China's Stock Market\")\n",
    "plt.xlabel('Quarter')  # 画图的x轴名称\n",
    "plt.ylabel('Return')  # 画图的y轴名称\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 长期预测 Long Horizon Forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "r_{t+1} + r_{t+2} + r_{t+3}  =\\alpha+\\beta x_{t}+\\varepsilon_{t+1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\admin\\AppData\\Local\\Temp\\ipykernel_11604\\690850194.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  reg_data['next_ret'] = reg_data['ret'].shift(-1) + 1\n",
      "C:\\Users\\admin\\AppData\\Local\\Temp\\ipykernel_11604\\690850194.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  reg_data['next_ret2'] = reg_data['ret'].shift(-2) + 1\n",
      "C:\\Users\\admin\\AppData\\Local\\Temp\\ipykernel_11604\\690850194.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  reg_data['next_ret3'] = reg_data['ret'].shift(-3) + 1\n",
      "C:\\Users\\admin\\AppData\\Local\\Temp\\ipykernel_11604\\690850194.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  reg_data['future_3month_return'] = reg_data['next_ret'] * reg_data['next_ret2'] * reg_data['next_ret3'] - 1\n"
     ]
    },
    {
     "data": {
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       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>MarketR_e</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>ret_e</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "      <th>Q</th>\n",
       "      <th>cpi</th>\n",
       "      <th>lcpi</th>\n",
       "      <th>lret</th>\n",
       "      <th>next_ret</th>\n",
       "      <th>next_ret2</th>\n",
       "      <th>next_ret3</th>\n",
       "      <th>future_3month_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2015-01-31</th>\n",
       "      <td>0.012618</td>\n",
       "      <td>0.080682</td>\n",
       "      <td>0.002263</td>\n",
       "      <td>0.010355</td>\n",
       "      <td>0.078419</td>\n",
       "      <td>0.214412</td>\n",
       "      <td>0.427916</td>\n",
       "      <td>0.204603</td>\n",
       "      <td>2015 Q1</td>\n",
       "      <td>0.7638</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.042797</td>\n",
       "      <td>1.151747</td>\n",
       "      <td>1.177800</td>\n",
       "      <td>0.414583</td>\n",
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       "    <tr>\n",
       "      <th>2015-02-28</th>\n",
       "      <td>0.045060</td>\n",
       "      <td>0.082388</td>\n",
       "      <td>0.002263</td>\n",
       "      <td>0.042797</td>\n",
       "      <td>0.080125</td>\n",
       "      <td>0.416276</td>\n",
       "      <td>0.197706</td>\n",
       "      <td>-0.111527</td>\n",
       "      <td>2015 Q1</td>\n",
       "      <td>1.4311</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.010355</td>\n",
       "      <td>1.151747</td>\n",
       "      <td>1.177800</td>\n",
       "      <td>1.082280</td>\n",
       "      <td>0.468143</td>\n",
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       "      <th>2015-03-31</th>\n",
       "      <td>0.153807</td>\n",
       "      <td>0.236307</td>\n",
       "      <td>0.002060</td>\n",
       "      <td>0.151747</td>\n",
       "      <td>0.234247</td>\n",
       "      <td>0.469904</td>\n",
       "      <td>-0.018104</td>\n",
       "      <td>-0.168588</td>\n",
       "      <td>2015 Q1</td>\n",
       "      <td>1.3758</td>\n",
       "      <td>0.007638</td>\n",
       "      <td>0.042797</td>\n",
       "      <td>1.177800</td>\n",
       "      <td>1.082280</td>\n",
       "      <td>0.920348</td>\n",
       "      <td>0.173177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-04-30</th>\n",
       "      <td>0.179860</td>\n",
       "      <td>0.193956</td>\n",
       "      <td>0.002060</td>\n",
       "      <td>0.177800</td>\n",
       "      <td>0.191896</td>\n",
       "      <td>0.173835</td>\n",
       "      <td>-0.195132</td>\n",
       "      <td>-0.177245</td>\n",
       "      <td>2015 Q2</td>\n",
       "      <td>1.5091</td>\n",
       "      <td>0.014311</td>\n",
       "      <td>0.151747</td>\n",
       "      <td>1.082280</td>\n",
       "      <td>0.920348</td>\n",
       "      <td>0.848690</td>\n",
       "      <td>-0.154641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2015-05-31</th>\n",
       "      <td>0.084202</td>\n",
       "      <td>0.326876</td>\n",
       "      <td>0.001922</td>\n",
       "      <td>0.082280</td>\n",
       "      <td>0.324954</td>\n",
       "      <td>-0.155219</td>\n",
       "      <td>-0.222180</td>\n",
       "      <td>-0.318855</td>\n",
       "      <td>2015 Q2</td>\n",
       "      <td>1.2308</td>\n",
       "      <td>0.013758</td>\n",
       "      <td>0.177800</td>\n",
       "      <td>0.920348</td>\n",
       "      <td>0.848690</td>\n",
       "      <td>0.856420</td>\n",
       "      <td>-0.331059</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>-0.033685</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>-0.034803</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "      <td>0.6000</td>\n",
       "      <td>0.002000</td>\n",
       "      <td>-0.000624</td>\n",
       "      <td>1.194874</td>\n",
       "      <td>0.995473</td>\n",
       "      <td>1.008606</td>\n",
       "      <td>0.199701</td>\n",
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       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.227078</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.225960</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.005000</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>0.995473</td>\n",
       "      <td>1.008606</td>\n",
       "      <td>0.996203</td>\n",
       "      <td>0.000228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.070220</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.069102</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>0.006000</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>1.008606</td>\n",
       "      <td>0.996203</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.045312</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.044194</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.2000</td>\n",
       "      <td>0.004000</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.996203</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>-0.040799</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>-0.041917</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "      <td>0.1000</td>\n",
       "      <td>0.003000</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>120 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR  MarketR_e   rfmonth       ret     ret_e  marketret3  \\\n",
       "month                                                                       \n",
       "2015-01-31  0.012618   0.080682  0.002263  0.010355  0.078419    0.214412   \n",
       "2015-02-28  0.045060   0.082388  0.002263  0.042797  0.080125    0.416276   \n",
       "2015-03-31  0.153807   0.236307  0.002060  0.151747  0.234247    0.469904   \n",
       "2015-04-30  0.179860   0.193956  0.002060  0.177800  0.191896    0.173835   \n",
       "2015-05-31  0.084202   0.326876  0.001922  0.082280  0.324954   -0.155219   \n",
       "...              ...        ...       ...       ...       ...         ...   \n",
       "2024-08-31 -0.031468  -0.033685  0.001118 -0.032586 -0.034803    0.151050   \n",
       "2024-09-30  0.195992   0.227078  0.001118  0.194874  0.225960    0.200147   \n",
       "2024-10-31 -0.003409   0.070220  0.001118 -0.004527  0.069102    0.000228   \n",
       "2024-11-30  0.009724   0.045312  0.001118  0.008606  0.044194         NaN   \n",
       "2024-12-31 -0.002679  -0.040799  0.001118 -0.003797 -0.041917         NaN   \n",
       "\n",
       "            marketret6  marketret12        Q     cpi      lcpi      lret  \\\n",
       "month                                                                      \n",
       "2015-01-31    0.427916     0.204603  2015 Q1  0.7638       NaN       NaN   \n",
       "2015-02-28    0.197706    -0.111527  2015 Q1  1.4311       NaN  0.010355   \n",
       "2015-03-31   -0.018104    -0.168588  2015 Q1  1.3758  0.007638  0.042797   \n",
       "2015-04-30   -0.195132    -0.177245  2015 Q2  1.5091  0.014311  0.151747   \n",
       "2015-05-31   -0.222180    -0.318855  2015 Q2  1.2308  0.013758  0.177800   \n",
       "...                ...          ...      ...     ...       ...       ...   \n",
       "2024-08-31         NaN          NaN  2024 Q3  0.6000  0.002000 -0.000624   \n",
       "2024-09-30         NaN          NaN  2024 Q3  0.4000  0.005000 -0.032586   \n",
       "2024-10-31         NaN          NaN  2024 Q4  0.3000  0.006000  0.194874   \n",
       "2024-11-30         NaN          NaN  2024 Q4  0.2000  0.004000 -0.004527   \n",
       "2024-12-31         NaN          NaN  2024 Q4  0.1000  0.003000  0.008606   \n",
       "\n",
       "            next_ret  next_ret2  next_ret3  future_3month_return  \n",
       "month                                                             \n",
       "2015-01-31  1.042797   1.151747   1.177800              0.414583  \n",
       "2015-02-28  1.151747   1.177800   1.082280              0.468143  \n",
       "2015-03-31  1.177800   1.082280   0.920348              0.173177  \n",
       "2015-04-30  1.082280   0.920348   0.848690             -0.154641  \n",
       "2015-05-31  0.920348   0.848690   0.856420             -0.331059  \n",
       "...              ...        ...        ...                   ...  \n",
       "2024-08-31  1.194874   0.995473   1.008606              0.199701  \n",
       "2024-09-30  0.995473   1.008606   0.996203              0.000228  \n",
       "2024-10-31  1.008606   0.996203        NaN                   NaN  \n",
       "2024-11-30  0.996203        NaN        NaN                   NaN  \n",
       "2024-12-31       NaN        NaN        NaN                   NaN  \n",
       "\n",
       "[120 rows x 16 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data['next_ret'] = reg_data['ret'].shift(-1) + 1\n",
    "reg_data['next_ret2'] = reg_data['ret'].shift(-2) + 1\n",
    "reg_data['next_ret3'] = reg_data['ret'].shift(-3) + 1\n",
    "reg_data['future_3month_return'] = reg_data['next_ret'] * reg_data['next_ret2'] * reg_data['next_ret3'] - 1\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             marketret3   R-squared:                       0.004\n",
      "Model:                            OLS   Adj. R-squared:                 -0.005\n",
      "Method:                 Least Squares   F-statistic:                    0.4639\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):              0.497\n",
      "Time:                        21:32:57   Log-Likelihood:                 93.155\n",
      "No. Observations:                 116   AIC:                            -182.3\n",
      "Df Residuals:                     114   BIC:                            -176.8\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0041      0.018     -0.236      0.813      -0.038       0.030\n",
      "lcpi           0.6011      0.883      0.681      0.496      -1.129       2.331\n",
      "==============================================================================\n",
      "Omnibus:                       18.137   Durbin-Watson:                   0.832\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               53.084\n",
      "Skew:                           0.455   Prob(JB):                     2.97e-12\n",
      "Kurtosis:                       6.187   Cond. No.                         87.7\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "#以2015年1月至2024年12月的reg_data为数据集\n",
    "#构建“3个月市场收益（marketret3）对滞后通胀（lcpi）”的普通最小二乘法（OLS）回归模型\n",
    "#cov_type='HAC'和maxlags=6采用异方差自相关一致（HAC）标准误估计\n",
    "model_cpi_3month = smf.ols('marketret3 ~ lcpi',\n",
    "                 data=reg_data['2015-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi_3month.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             marketret6   R-squared:                       0.105\n",
      "Model:                            OLS   Adj. R-squared:                  0.097\n",
      "Method:                 Least Squares   F-statistic:                     4.732\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):             0.0317\n",
      "Time:                        21:32:58   Log-Likelihood:                 95.707\n",
      "No. Observations:                 113   AIC:                            -187.4\n",
      "Df Residuals:                     111   BIC:                            -182.0\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.0524      0.031     -1.675      0.094      -0.114       0.009\n",
      "lcpi           3.1175      1.433      2.175      0.030       0.309       5.927\n",
      "==============================================================================\n",
      "Omnibus:                        2.516   Durbin-Watson:                   0.491\n",
      "Prob(Omnibus):                  0.284   Jarque-Bera (JB):                2.347\n",
      "Skew:                          -0.271   Prob(JB):                        0.309\n",
      "Kurtosis:                       2.548   Cond. No.                         87.9\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "#构建“6个月市场收益（marketret6）对滞后通胀（lcpi）”的普通最小二乘法（OLS）回归模型\n",
    "\n",
    "model_cpi_6month = smf.ols('marketret6 ~ lcpi',\n",
    "                 data=reg_data['2015-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpi_6month.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:            marketret12   R-squared:                       0.230\n",
      "Model:                            OLS   Adj. R-squared:                  0.222\n",
      "Method:                 Least Squares   F-statistic:                     11.62\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):           0.000927\n",
      "Time:                        21:32:59   Log-Likelihood:                 66.884\n",
      "No. Observations:                 107   AIC:                            -129.8\n",
      "Df Residuals:                     105   BIC:                            -124.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept     -0.1088      0.044     -2.473      0.013      -0.195      -0.023\n",
      "lcpi           6.4559      1.894      3.409      0.001       2.744      10.168\n",
      "==============================================================================\n",
      "Omnibus:                        2.352   Durbin-Watson:                   0.425\n",
      "Prob(Omnibus):                  0.308   Jarque-Bera (JB):                2.032\n",
      "Skew:                          -0.337   Prob(JB):                        0.362\n",
      "Kurtosis:                       3.048   Cond. No.                         91.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "#构建“12个月市场收益（marketret12）对滞后通胀（lcpi）”的普通最小二乘法（OLS）回归模型\n",
    "\n",
    "model_cpi_12month = smf.ols('marketret12 ~ lcpi',\n",
    "                 data=reg_data['2015-01':'2024-12']).fit(       \n",
    "                        cov_type='HAC', cov_kwds={'maxlags': 6})    \n",
    "print(model_cpi_12month.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 整理结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                         Table - OLS Regressions: Forecast Stock Market Return\n",
      "=======================================================================================================\n",
      "                 Next Month's Return Next 3 Months' Return Next 6 Months' Return Next 12 Months' Return\n",
      "-------------------------------------------------------------------------------------------------------\n",
      "Intercept        0.002               -0.004                -0.052*               -0.109**              \n",
      "                 (0.007)             (0.018)               (0.031)               (0.044)               \n",
      "lcpi             0.040               0.601                 3.118**               6.456***              \n",
      "                 (0.253)             (0.883)               (1.433)               (1.894)               \n",
      "R-squared        0.000               0.004                 0.105                 0.230                 \n",
      "R-squared Adj.   -0.009              -0.005                0.097                 0.222                 \n",
      "No. observations 118                 116                   113                   107                   \n",
      "=======================================================================================================\n",
      "Standard errors in parentheses.\n",
      "* p<.1, ** p<.05, ***p<.01\n"
     ]
    }
   ],
   "source": [
    "#导入statsmodels库中用于合并回归结果的工具summary_col\n",
    "from statsmodels.iolib.summary2 import summary_col\n",
    "\n",
    "#定义用于汇总表格的信息项\n",
    "info_dict = {'No. observations': lambda x: f\"{int(x.nobs):d}\"}\n",
    "\n",
    "#将“月度、3个月、6个月、12个月市场收益对滞后通胀”的四个回归模型结果合并，设置数据格式、模型名称、信息字典及变量顺序等参数\n",
    "results_table = summary_col(results=[model_cpi, model_cpi_3month, model_cpi_6month, model_cpi_12month],\n",
    "                            float_format='%0.3f', #数据显示的格式，默认四位小数\n",
    "                            stars=True, # 是否有*，True为有\n",
    "                            model_names=[\"Next Month's Return\", \"Next 3 Months' Return\", \"Next 6 Months' Return\", \"Next 12 Months' Return\"],\n",
    "                            info_dict=info_dict,\n",
    "                            regressor_order=['Intercept', 'lcpi'])\n",
    "\n",
    "#添加标题并输出\n",
    "results_table.add_title(\n",
    "    'Table - OLS Regressions: Forecast Stock Market Return')\n",
    "\n",
    "print(results_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# CPI的自相关性"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    cpi   R-squared:                       0.826\n",
      "Model:                            OLS   Adj. R-squared:                  0.824\n",
      "Method:                 Least Squares   F-statistic:                     355.2\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):           3.04e-37\n",
      "Time:                        21:33:03   Log-Likelihood:                -81.577\n",
      "No. Observations:                 119   AIC:                             167.2\n",
      "Df Residuals:                     117   BIC:                             172.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.1331      0.073      1.832      0.067      -0.009       0.276\n",
      "lcpi           0.9133      0.048     18.846      0.000       0.818       1.008\n",
      "==============================================================================\n",
      "Omnibus:                        5.655   Durbin-Watson:                   1.862\n",
      "Prob(Omnibus):                  0.059   Jarque-Bera (JB):                8.383\n",
      "Skew:                          -0.102   Prob(JB):                       0.0151\n",
      "Kurtosis:                       4.284   Cond. No.                         4.00\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\admin\\AppData\\Local\\Temp\\ipykernel_11604\\2061533061.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  reg_data['lcpi'] = reg_data['cpi'].shift(1)\n"
     ]
    }
   ],
   "source": [
    "#创建滞后1期的通胀变量lcpi，用于捕捉通货膨胀的自相关性\n",
    "reg_data['lcpi'] = reg_data['cpi'].shift(1)\n",
    "\n",
    "#构建“当前通胀（cpi）对滞后通胀（lcpi）”的普通最小二乘法（OLS）回归模型\n",
    "model_cpiself = smf.ols('cpi~lcpi',\n",
    "                 data=reg_data['2015-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpiself.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    ret   R-squared:                       0.001\n",
      "Model:                            OLS   Adj. R-squared:                 -0.008\n",
      "Method:                 Least Squares   F-statistic:                    0.1826\n",
      "Date:                Thu, 16 Oct 2025   Prob (F-statistic):              0.670\n",
      "Time:                        21:33:03   Log-Likelihood:                 164.60\n",
      "No. Observations:                 120   AIC:                            -325.2\n",
      "Df Residuals:                     118   BIC:                            -319.6\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0055      0.007      0.847      0.397      -0.007       0.018\n",
      "cpi           -0.0013      0.003     -0.427      0.669      -0.007       0.005\n",
      "==============================================================================\n",
      "Omnibus:                       13.407   Durbin-Watson:                   1.707\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               44.069\n",
      "Skew:                          -0.016   Prob(JB):                     2.70e-10\n",
      "Kurtosis:                       5.969   Cond. No.                         3.96\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "#构建“当月收益率（ret）对当月通胀（cpi）”的普通最小二乘法（OLS）回归模型\n",
    "model_cpiself = smf.ols('ret~cpi',\n",
    "                 data=reg_data['2015-01':'2024-12']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_cpiself.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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